If you haven’t done so yet, separate the eggs first. Separate 1 egg white in a small bowl, then place the egg white in your heatproof mixing bowl. Repeat with the remaining egg whites. This way, if a yolk breaks in one of them, you don’t waste the whole batch.
Whisk sugar into the egg whites, then set the bowl over a saucepan filled with just two inches of simmering water over medium heat. Do not let the bottom of the egg whites bowl touch the water. Whisk the whites and sugar constantly until sugar is dissolved and mixture has thinned out, about 4 minutes. The mixture will be thick and tacky at first, then thin out and be frothy white on top. To test that it’s ready, you can use your finger or an instant read thermometer. Lightly and quickly dip your finger (it’s very hot, be careful) and rub the mixture between your thumb and finger. You shouldn’t feel any sugar granules. If using a thermometer, the temperature should read 160°F (71°C).
No need to let it cool down to start this next step– it’s important to begin mixing while it is still warm. Transfer mixture to the bowl of a stand mixer fitted with a whisk attachment (if you aren’t already using the metal bowl that comes with it). You can use a hand mixer instead, but this step takes awhile and your arm tires quickly. On medium-high speed, beat the mixture until stiff glossy peaks form and the meringue is no longer warm to the touch, at least 10-15 minutes.
If the bowl and meringue still feel warm, wait until both cool to room temperature (around 70°F (21°C)) before adding the butter in the next step. Feel free to place it in the refrigerator. A warm bowl and meringue will melt the butter.
Switch the stand mixer to the paddle attachment. On medium-high speed, add the butter 1 tablespoon at a time. Wait for the butter to fully mix in before adding the next tablespoon. After all the butter has been added, turn the mixer down to medium speed and fully beat in the vanilla and salt, about 30 seconds.
Your Swiss meringue buttercream should be thick, creamy, and silky smooth and is ready to use on your cake.